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A137785
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Triangular sequence of coefficients of the expansion of the complex dynamics Lattes function: p(x,t)=Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2)).
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0, 1, 6, 0, 1, 0, 18, 0, 1, 96, 0, 36, 0, 1, 0, 480, 0, 60, 0, 1, 2880, 0, 1440, 0, 90, 0, 1, 0, 20160, 0, 3360, 0, 126, 0, 1, 161280, 0, 80640, 0, 6720, 0, 168, 0, 1, 0, 1451520, 0, 241920, 0, 12096, 0, 216, 0, 1, 14515200, 0, 7257600, 0, 604800, 0, 20160, 0, 270, 0, 1
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Row sums are:
{1, 7, 19, 133, 541, 4411, 23647, 248809, 1705753, 22398031, 187640971};
This function is called Samuel Lattes' function by Mandelbrot
and it's inverse in Hill is Onsager's k1 associated with the two dimensional
crystal. I have exchanged the constant in each of these equations for an Exp[x*t]
to get my expansion function. The dynamics associated with this function are
chaotic. It also seems to be strongly associated with the magnetization
function A136264.
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REFERENCES
| The Beauty of Fractals, Springer-Verlag, New York, 1986, editors Peitgen and Richter, pages 153
Terrell Hill, Statistical Mechanics, Dover, 1987, page 329 ff
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FORMULA
| p(x,t)=Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2))=Sum(P(x,n)8t^n/n1,{n,0,Infinity}); out_n,m=(n+1)!*Coefficient(P(x,n)).
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EXAMPLE
| {0, 1},
{6, 0, 1},
{0, 18, 0, 1},
{96, 0, 36, 0, 1},
{0, 480, 0, 60, 0, 1},
{2880, 0, 1440, 0, 90, 0, 1},
{0, 20160, 0, 3360, 0, 126, 0, 1},
{161280, 0, 80640, 0, 6720, 0, 168, 0, 1},
{0, 1451520, 0, 241920, 0, 12096, 0, 216, 0, 1},
{14515200, 0, 7257600, 0, 604800, 0, 20160, 0, 270, 0, 1},
{0, 159667200, 0, 26611200, 0, 1330560, 0, 31680, 0, 330, 0, 1}
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MATHEMATICA
| p[t_] = Exp[x*t]*(1 + t^2)^2/(t*(1 - t^2)); Table[ ExpandAll[(n + 1)!*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]], { n, 0, 10}]; a = Table[(n + 1)!* CoefficientList[SeriesCoefficient[ Series[p[t], {t, 0, 30}], n], x], {n, 0, 10}]; Flatten[a]
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CROSSREFS
| Cf. A136264.
Sequence in context: A084680 A051626 A200229 * A199568 A134899 A076413
Adjacent sequences: A137782 A137783 A137784 * A137786 A137787 A137788
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KEYWORD
| nonn,tabl,uned
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AUTHOR
| Roger L. Bagula (rlbagulatftn(AT)yahoo.com), Apr 28 2008
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